TY - JOUR
T1 - Feature extraction for functional time series
T2 - Theory and application to NIR spectroscopy data
AU - Yang, Yang
AU - Yang, Yanrong
AU - Shang, Han Lin
N1 - Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2022/5
Y1 - 2022/5
N2 - We propose a novel method to extract global and local features of functional time series. The global features concerning the dominant modes of variation over the entire function domain, and local features of function variations over particular short intervals within function domain, are both important in functional data analysis. Functional principal component analysis (FPCA), though a key feature extraction tool, only focus on capturing the dominant global features, neglecting highly localized features. We introduce a FPCA-BTW method that initially extracts global features of functional data via FPCA, and then extracts local features by block thresholding of wavelet (BTW) coefficients. Using Monte Carlo simulations, along with an empirical application on near-infrared spectroscopy data of wood panels, we illustrate that the proposed method outperforms competing methods including FPCA and sparse FPCA in the estimation functional processes. Moreover, extracted local features inheriting serial dependence of the original functional time series contribute to more accurate forecasts. Finally, we develop asymptotic properties of FPCA-BTW estimators, discovering the interaction between convergence rates of global and local features.
AB - We propose a novel method to extract global and local features of functional time series. The global features concerning the dominant modes of variation over the entire function domain, and local features of function variations over particular short intervals within function domain, are both important in functional data analysis. Functional principal component analysis (FPCA), though a key feature extraction tool, only focus on capturing the dominant global features, neglecting highly localized features. We introduce a FPCA-BTW method that initially extracts global features of functional data via FPCA, and then extracts local features by block thresholding of wavelet (BTW) coefficients. Using Monte Carlo simulations, along with an empirical application on near-infrared spectroscopy data of wood panels, we illustrate that the proposed method outperforms competing methods including FPCA and sparse FPCA in the estimation functional processes. Moreover, extracted local features inheriting serial dependence of the original functional time series contribute to more accurate forecasts. Finally, we develop asymptotic properties of FPCA-BTW estimators, discovering the interaction between convergence rates of global and local features.
KW - Functional principal component analysis
KW - Long-run covariance estimation
KW - Near-infrared spectroscopy data
KW - Regularized wavelet approximation
UR - http://www.scopus.com/inward/record.url?scp=85118987752&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2021.104863
DO - 10.1016/j.jmva.2021.104863
M3 - Article
SN - 0047-259X
VL - 189
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
M1 - 104863
ER -